Answered

The slope-intercept form of a linear equation is [tex]y = mx + b[/tex], where [tex]x[/tex] and [tex]y[/tex] are coordinates of an ordered pair, [tex]m[/tex] is the slope of the line, and [tex]b[/tex] is where the line crosses the [tex]y[/tex]-axis.

Which is an equivalent equation solved for the slope, [tex]m[/tex]?

A. [tex]m = yx + b[/tex]
B. [tex]m = \frac{y - b}{x}[/tex]
C. [tex]m = \frac{y}{x} - b[/tex]
D. [tex]m = y - \frac{b}{x}[/tex]



Answer :

GinnyAnswer
Sure, let's solve for the slope [tex]\( m \)[/tex] in the equation [tex]\( y = mx + b \)[/tex].

Given the equation,
[tex]\[ y = mx + b, \][/tex]
we need to isolate [tex]\( m \)[/tex].

Step 1: Subtract [tex]\( b \)[/tex] from both sides of the equation.

[tex]\[ y - b = mx + b - b \][/tex]

Simplifying, we get:

[tex]\[ y - b = mx \][/tex]

Step 2: Divide both sides by [tex]\( x \)[/tex] to isolate [tex]\( m \)[/tex].

[tex]\[ \frac{y - b}{x} = m \][/tex]

Rewriting this, we get:

[tex]\[ m = \frac{y - b}{x} \][/tex]

So, the equivalent equation solved for the slope [tex]\( m \)[/tex] is:

[tex]\[ m = \frac{y - b}{x} \][/tex]

Therefore, the correct choice is:
[tex]\[ \boxed{m = \frac{y - b}{x}} \][/tex]